Brain functions such as information processing, memory formation and motor control often involve oscillatory neuronal networks. Mathematical modeling has been particularly useful in gaining insights into how such oscillations are generated and how they contribute to nervous system function. Dynamic current clamp techniques (Sharp et al, 1993) that permit the interactions of computer models and neuronal networks through artificial synapses have opened up a new form of modeling, hybrid systems analysis. Recent progress in computer hardware makes incorporation of biophysically realistic mathematical models of neurons and networks into hybrid systems feasible. Still, hybrid systems are difficult to construct without model simplification. Analog very large-scale integrated circuit (aVLSI) models overcome the speed limitation of digital models, but until now very few aVLSI models have been as realistic or as amenable to parameter variations as their digital counterparts. Especially in studies of oscillatory neural networks, hybrid system having a model neuron connected to real counterpart combines advantages of mathematical modeling and real electrophysiological experiments. In the R21 phase, we will expand upon our research on a neuronal network that times heartbeat in the leech toward the goal of developing useful hybrid systems for the study of oscillation in neuronal networks. Aim 1. Development of a real-time dynamic clamp and a mathematical model of heart interneuron model cell running in real-time on a controller board. Aim 2. Development of an aVLSI (silicon) heart interneuron model. Aim 3. Construction of hybrid systems for studying half-center oscillators underlying leech heartbeat central pattern generation. Once these tools are developed, we will use them in the R33 phase to explore basic questions about the generation of oscillation in mutually inhibitory neuronal networks. Aim 1: Continue the development of the silicon models of a HN neuron and thoroughly ascertain their dynamics. Aim 2: Analyze dynamic behaviors of the silicon and living neurons using a controller board based dynamic clamp. Aim 3: Explore systematically the dynamics of hybrid half-center oscillators. The development of such tools will make hybrid system analysis easily accessible and thus further our insights into neuronal network dynamics in a variety of preparations.